My Math Forum Price Elasticity, Separation of Variables

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 March 16th, 2012, 08:46 PM #1 Member   Joined: Sep 2010 Posts: 63 Thanks: 0 Price Elasticity, Separation of Variables So I naively took price elasticity http://en.wikipedia.org/wiki/Price_elasticity_of_demand http://en.wikipedia.org/wiki/Elasticity_%28economics%29 Ed = ((Qd-Qo)/Qd)/((Pd-Po)/Pd)) In the differential form: Ed = (P/Q)*dQ/dP Separated variables: (Ed/P)dP = (1/Q)dQ Integrated the left from Po to P and the right from Qo to Q and got the incredibly borrowing result: exp(Ed)(P/Po)=Q/Qo Which essentially says that the only functions that can satisfy constant price elasticity are a non negative slopping line though the origin. Now, this result is disappointing because this does not look like a typical demand curve at all, yet price elasticity is used to consider effects on total revenue due to changes in quantities: http://en.wikipedia.org/wiki/Total_revenue_test I was expecting a function that would be able to interpolate a demand function well so I could approximate a small a small region of the curve with constant elasticity. I could use the non differential form but I was expecting them to agree over a small region and am wondering what I might have done wrong. Reviewing separation of variables: http://en.wikipedia.org/wiki/Separation_of_variables I see I forgot an absolute value sign. This will also gives me negative slope solutions but I'm still restricted to lines that go though the origin. : Pauses and scratches head :

 Tags elasticity, price, separation, variables

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